Side Content enables you to create widgets which have different content on different pages.
If you see an error message like "Parse error: parse error, unexpected T_STRING, expecting T_OLD_FUNCTION or T_FUNCTION or T_VAR ..." it is because you are running under PHP4. The plugin requires PHP5.
As of release 0.6, yes, it should work under WP-MU, although it has only been tested with the 2.6.3 release, and not very extensively.
Yes. There's an option on the settings page (Options - Side Content) for this.
The plugin uses custom fields to store the widget code, but has its own subpanel for editing to improve ease of use. You can use either to edit your widgets but it is best to stick to one or the other.
Not all plugins use the new WP Shortcode API yet. If you need particular shortcodes to be recognised it may be possible to have an addon developed for that purpose. Contact the author for more details.
There are no plans to add PHP execution support to the plugin. In my opinion this would not be a good way to use it. Most of those who have requested the feature are actually looking for what is offered by the Widget Logic plugin, the ability to hide or display content conditionally.